Nope, herpes doesn't appear in the armpits ever.
The only exception may be is if you're a wrestler or are involved in other contact sports where not a lot of clothing is worn, and get something called herpes gladiatorum, https://www.healthline.com/health/herpes-gladiatorum
Herpes infects nerve groups, and oral herpes infects the trigeminal nerve, which means only your mouth and nose (and your eyes sometimes) can be infected. Genital herpes infects your sacral ganglia, which means only the area covered by boxer shorts would be affected.
You can get infected hair follicles, boils, abscesses, and a lot of other things under your arms. You should let your doctor see what you have going on.